Quasi-invariant measures and maximal algebras on minimal flows.

Admissible vector fields and quasi-invariant measures∗

Stationary flows and uniqueness of invariant measures

In this short paper, we consider a quadruple (Ω,A , θ, μ), where A is a σ-algebra of subsets of Ω, and θ is a measurable bijection from Ω into itself that preserves the measure μ. For each B ∈ A , we consider the measure μB obtained by taking cycles (excursions) of iterates of θ from B. We then derive a relation for μB that involves the forward and backward hitting times of B by the trajectory ...

Absolutely Continuous Invariant Measures That Are Maximal

Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.

On Maximal Functions over Circular Sectors with Rotation Invariant Measures

Given a rotation invariant measure in Rn, we define the maximal operator over circular sectors. We prove that it is of strong type (p, p) for p > 1 and we give necessary and sufficient conditions on the measure for the weak type (1, 1) inequality. Actually we work in a more general setting containing the above and other situations. Let X be a topological space and μ be a Borel measure on X. By ...

On semi maximal filters in BL-algebras

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...